\name{degp3}
\alias{degp3}
\alias{pegp3}
\alias{qegp3}
\alias{regp3}
\title{ Density, cumulative density, quantiles and random number generation
        for the extended generalized Pareto distribution 3}
\description{
  Density, cumulative density, quantiles and random number generation
        for the EGP3 distribution of Papastathopoulos and Tawn
}
\usage{
degp3(x, kappa=1, sigma, xi, u = 0, log.d = FALSE)
pegp3(q, kappa=1, sigma, xi, u = 0, lower.tail = TRUE, log.p = FALSE)
qegp3(p, kappa=1, sigma, xi, u = 0, lower.tail = TRUE, log.p = FALSE)
regp3(n, kappa=1, sigma, xi, u = 0)
}
%- maybe also 'usage' for other objects documented here.
\arguments{
  \item{x, q, p}{ Value, quantile or probability respectively. }
  \item{n}{ Number of random numbers to simulate.}
  \item{kappa}{The power parameter (Papastathopoulos and Tawn call it the shape parameter
               and call what we call the shape parameter the tail index.)}
  \item{sigma}{Scale parameter.}
  \item{xi}{Shape parameter.}
  \item{u}{Threshold}
  \item{log.d, log.p}{Whether or not to work on the log scale.}
  \item{lower.tail}{Whether to return the lower tail.}
}
\references{
I. Papastathopoulos and J. A. Tawn, Extended generalized Pareto modles for
tail estimation, Journal of Statistical Planning and Inference, 143, 131 -- 143,
2013
}

\author{Harry Southworth}
\examples{
  x <- regp3(1000, kappa=2, sigma=1, xi=.5)
  hist(x)
  x <- regp3(1000, kappa=2, sigma=exp(rnorm(1000, 1, .25)), xi=rnorm(1000, .5, .2))
  hist(x)
  plot(pegp3(x, kappa=2, sigma=1, xi=.5))
}
\keyword{ models }

